03 December 1994


To the many friends of Professor Charles Cullen, and to Charlie himself,
I offer this appreciation on the occasion of his retirement:


I actually started working with Charlie Cullen before ever taking a class
from him.  He was teaching a variety of linear algebra classes to 
undergraduates, and wanted to expose his students to the great works
of LINPACK and EISPACK.  But he didn't want to spend a lot of class time
teaching his students the innards of FORTRAN, and then debugging their
programs.  I imprudently suggested that it couldn't be hard to write
an interactive program that would let the student type in a matrix and
choose the desired operations, after which the program would take care
of calling the software in the correct way, and displaying the results.
Charlie called my bluff, and I've spent a considerable portion of the next 
15 years trying to make him happy.


Since then, he's been my teacher, examiner, friend and counselor,
and I've come to know a little bit about him.  If I had to pick
his most outstanding feature, I would be tempted to say it was
his concern for the students, but I don't think that's quite right;
Charlie never meant to be a social worker.  His goal was never to
make the students see him as his friend; in fact, he quite frequently
complained if he felt that his students were not trying to learn.
He refused to lower his standards or accept inferior work.  Charlie
was quite clear that his absolutely main concern was teaching.


Perhaps I can suggest something of what Charlie meant by good teaching
by recounting an incident that occurred while I was developing 
the MATMAN code for his linear programming class.
 
MATMAN allowed the student to type in a test matrix, and then
laboriously transform the matrix into row reduced echelon form,
by rescaling rows, interchanging them, and adding a multiple of
one row to another.

I was trying to improve MATMAN, but every time I made a change, I
had to check that MATMAN was still healthy by putting in a test
matrix myself, and going through the same tedious steps.  Finally,
I came up with a way for the program to do the transformation automatically.  
All I had to do was type in the matrix, request the transformation,
and watch.  I was thrilled with this new feature, and figured the
students would love it too.  I went ahead and replaced the old version 
without telling Charlie about it.
 
A few days later, I ran across Charlie in the hall, and asked him
how he like the new feature.  

  "Oh, I want you to take that out immediately."  

  "What?" I said, "what's the matter, doesn't it work?"  

  "Of course it works", he said, "that's the problem.  It's terrible 
  pedagogy.  The whole point of this exercise is to do the arithmetic
  for the students, but make them choose the operations, one by one, 
  so that they understand the steps in the process.  If you do it all
  for them, they'll ignore it just like they ignore the book."

I never forgot his lesson: a teacher who is TOO helpful can hurt the 
students very badly.


Despite his occasionally gruff exterior, Charlie is very generous with
his time and attention.  His students have many kindnesses to be grateful
for.  On my own behalf, I am thankful for his frequent urgings that I try 
again for a degree; I'm glad I listened, since I expect to graduate
this spring.  


And finally, of course, I should point out some off-the-wall, yet
mathematical, benefits of working with Charlie:


  I knew he was a sailor, of course, and, one day, after much thought, 
  I was brave enough to go into his office to discuss a matter of much
  concern to me:  I could prove that nobody can sail against the wind:
  not Columbus, not Ted Turner, not Charlie.  Charlie did chuckle, but 
  then he sat me and sketched out an explanation involving airfoils.  
  But he wasn't satisfied just to see me nodding, so a short while later 
  he took me out on his boat up in Moraine State Park.  It was a sobering 
  experience to see the shore slipping away; I still didn't believe he
  could get us back.  "Here," said Charlie, handing me the ropes.  "It's
  all yours."
  

  And then there was his work in Poisson transport phenomena, better
  known as the Thursday fish sandwich run.  While we were exiled up in 
  MIB, he took it upon himself to keep a weekly lunch going.  He had to take
  the orders, gather the money, and drive downtown for the food.
  He always brought back just the right number and kind of sandwiches.
  For some reason, though, the mound of leftover condiments in the 
  refrigerator seemed to grow without bounds.  But he calmed my fears 
  by pointing out that every packet of tartar sauce in would eventually 
  get used, if only we numbered them and used them in sequence.


  And lastly, of course, there was his mystifying question, appearing
  in several editions of his books: "What do eigenvalues and liverwurst
  have in common?"  


It's a good thing Charlie got me into eigenvalues before I ever saw that
that question, because, you see, I know I don't like liverwurst!


With affection and high regards,

John Burkardt